The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

PROP. III. To find the Height of an House, Steeple, Tower, or Tree, from the Ground, at one Observation; and the length of the Ladder which will Scale it.

If you can approach the bottom or foot of the Thing whose Height you desire, the thing is easily performed by this Quadrant or Cross-Staff, holding up your Qua∣drant to the Place whose Height you would know, and looking through the Sight on the Side EC, going nearer or further from it, till the Thred cut 45 deg. or fall upon 100 Parts in the Quadrat: So shall the Height of the Thing above the level of your Eye, be equal to the Distance between the Place and your Eye.

If the Thred fall on 50 parts of a right Shadow, or 26 deg. ½ or Vanes on the Cross-Staff, set to the Number of Deg. the Height is but half the Distance.

If the Thred cut 25 Parts in the Quadrat, or 13 deg. 55 min. in the Arch of the Quadrant, it is but a quarter of the Distance: But if it fall on 75 Parts, or 36 deg. 53, it is three quarters of the Distance. The Rule is,

As 100, to the Parts on which the Thred falleth:

So is the Distance, to the Height required.

And on the contrary,

As the Parts cut by the Thred, are to 100:

So is the Height, to the Distance.

[illustration] geometrical diagram

But when the Thred shall fall on the parts of the contrary Shadow, if it fall on 50 Parts, or 63 deg. 30 min. as it doth at C, the Height is double unto the Distance CD. If on 25, it is four times the Distance. If the Thred fall upon the contrary Shadow, this is the Rule,

As the Parts cut by the Thred, are unto 100:

So is the Distance, unto the Height.

On the contrary,

As 100, are unto the Parts cut by the Thred:

So is the Height, unto the Distance.

These are the Rules Mr. Gunter shews by the Quadrat, And what hath been said

of Height and Distance, the same may be understood of Height and Shadow; but here follows more useful Rules than these before-going.